Elliptic curve isogeny class 28224.7-i over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-28224.7-i
• Conductor: 28224.7
• Rank: \( 1 \)

Base field \(\Q(\sqrt{-7}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x + 2 \); class number \(1\).

Elliptic curves in class 28224.7-i over \(\Q(\sqrt{-7}) \)

Isogeny class 28224.7-i contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
28224.7-i1	\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -4 a + 3\) , \( 2 a - 3\bigr] \)
28224.7-i2	\( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 3 a + 2\) , \( -7\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph